Mr Cameron, who had been planning to stay in Paris overnight after meeting the French president, has returned to Downing Street

In a joint press conference, Mr Hollande said he wanted to express his solidarity with the UK after the "murder of a British soldier", but Mr Cameron did not confirm the victim had been a serviceman

At a meeting of the government's emergency response committee, Cobra, it was decided to tighten security at Woolwich and other barracks in London

The Ministry of Defence said it was urgently looking into reports the incident had involved a soldier

Another Cobra meeting will be held on Thursday morning, chaired by Mr Cameron

Home Secretary Theresa May said she had been briefed by the director general of Security Service MI5, Andrew Parker, and Metropolitan Police Commissioner Bernard Hogan-Howe on the "sickening and barbaric" attack.

Mr Cameron said Britain had faced "these sort of attacks", adding: "We will never buckle in the face of them.

"People across Britain, people in every community, I believe, will utterly condemn this attack."

He expressed sympathy for the victim and his family, saying: "It is the most appalling crime. We are obviously seeking, and the police are urgently seeking, the full facts about this case."

One witness, identified only as James, said two men had attacked another man, aged about 20, who was wearing a T-shirt of military charity Help for Heroes.

"These two guys were crazed. They were just animals. They dragged him from the pavement and dumped his body in the middle of the road and left his body there," he told LBC radio.

He said after the "horrendous" attack, the two men, who were also in their 20s, stood around, waving knives and a gun, and asked people to take pictures of them "as if they wanted to be on TV or something".

Analysis

By Dominic CascianiHome affairs correspondent

The case for this being a jihadist attack, following the ideology of al-Qaeda, is compelling - even if the police won't yet say so officially.

If it is, then it would be the first such incident leading to a death of someone other than the perpetrator since the 2005 London suicide bombings.

So the first task for ministers and officials is to assess the threat to the public - are other attacks planned?

The official terrorism threat level is currently "substantial", which means an attack is "a strong possibility".

If officials raise the level to "severe", that would mean they fear another attack is highly likely.

If the victim is indeed a soldier, then that will be no surprise to security chiefs.

Jihadists believe they are at war with the military because of its role in the Afghanistan conflict and elsewhere.

The UK has previously uncovered three plots linked to possible terror attacks on the armed forces, including a cell in 2007 which planned to kidnap and behead a soldier in an Iraq-style hostage video.

"They were oblivious to anything, they were more worried about having their photo taken, running up and down the road," he said.

Witness Graham Wilders told the BBC he had arrived on the scene to find a car crashed into a wall and a man on the ground.

"Two people were lying over him and I thought they were trying to resuscitate him," he said.

But Mr Wilders said he had driven on to park his car, and when he had returned another witness had told him the two men had been stabbing the man on the ground.

Thomas, another witness who contacted the BBC, said: "I got there minutes after it happened because you could hear gunshots from Woolwich High Street.

"Basically two men carried out an axe attack on a young army cadet walking along the street, by the looks of things the police responded and then shot them in front of the public, at the same time I couldn't really tell if the cadet was fatally or not hurt as police were crowded around him."

According to senior Whitehall sources the people carrying out the attack were heard to say: "Allahu Akbar [God is Great]", BBC political editor Nick Robinson reported.

Met Police Commissioner Bernard Hogan-Howe said it was "hard to comprehend the shocking and horrific scenes we have seen this afternoon on a busy street as Londoners went about their day as normal".

He said officers would "work tirelessly to uncover why this occurred and who was responsible".

On Twitter, the Mayor of London Boris Johnson described the attack as a "sickening deluded and unforgivable act of violence".

Buckingham Palace says the Queen is concerned at the news of the attack and is being kept informed.

Help for Heroes said the charity was "appalled to hear that a man, believed to be a serving soldier, has been brutally murdered in Woolwich today".

The Muslim Council of Britain said in a statement: "This is a truly barbaric act that has no basis in Islam and we condemn this unreservedly. Our thoughts are with the victim and his family."

School lock-down

Mr Raynsford, the Woolwich and Greenwich MP, said he had spoken to local police and understood a number of weapons had been seized at the scene including a gun, knives, and a machete.

Metropolitan Police Commander Simon Letchford said two alleged attackers had been shot by officers.

He said: "Police were called to reports of an assault... where one man was being assaulted by two other men. A number of weapons were reportedly being used in the attack, and this included reports of a firearm.

"Officers including local Greenwich officers arrived at the scene, and shortly after firearms officers arrived on the scene.

"On their arrival at the scene they found a man, who was later pronounced dead.

"Two men, who we believe from early reports to have been carrying weapons, were shot by police. They have both been taken to separate London hospitals. They are receiving treatment for their injuries.

"I can understand that this incident will cause community concerns and I would like to reiterate that we are investigating the circumstances."

Meanwhile, the Independent Police Complaints Commission (IPCC) confirmed it had been informed.

David Dixon, a local head teacher, told the BBC News Channel he walked out of the school gates and saw a body lying in the road a short distance away.

He then heard gunshots and instructed staff to lock all the gates of his school.

An air ambulance landed in the playground and the children were sent home.

The Met Police said extra officers would remain on duty in the London borough of Greenwich on Wednesday night.